Optimizing tradeoffs among housing sustainability objectives

Automation in Construction 53 (2015) 83–94

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Automation in Construction journal homepage: www.elsevier.com/locate/autcon

Optimizing tradeoffs among housing sustainability objectives Aslihan Karatas a,1, Khaled El-Rayes b,⁎ a b

Postdoctoral Research Fellow, Dept. of Civil and Environmental Engineering, University of Michigan, MI, 48109, United States Professor, Dept. of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, IL 61801, United States

a r t i c l e

i n f o

Article history: Received 13 March 2014 Received in revised form 13 November 2014 Accepted 26 February 2015 Available online 21 March 2015 Keywords: Sustainability Housing units Multi-objective optimization Environmental performance Social quality of life Life cycle cost Genetic algorithm

a b s t r a c t The sustainability of housing units can be improved by integrating green building equipment and systems such as energy-efficient HVAC systems, building envelopes, water heaters, appliances, and water-efficient fixtures. The use of these green building measures often improves the environmental and social performances of housing units; however they can increase their initial cost and life cycle cost. This paper presents a multi-objective optimization model that is capable of optimizing housing design and construction decisions in order to generate optimal/near-optimal tradeoffs among the three sustainability objectives of maximizing the operational environmental performance of housing units, maximizing the social quality of life for their residents, and minimizing their life cycle cost. The model is designed as a multi-objective genetic algorithm to provide the capability of optimizing multiple housing objectives and criteria that include minimizing carbon footprint and water usage during housing operational phase, maximizing thermal comfort, enhancing indoor air and lighting quality, improving neighborhood quality, and minimizing life cycle cost. An application example is analyzed to illustrate the use of the developed model and evaluate its performance. The results of this analysis illustrate the novel capabilities of the model in generating 210 near-optimal tradeoff solutions for the analyzed housing example, where each represents an optimal/near-optimal and unique tradeoff among the aforementioned three sustainability optimization objectives of maximizing the operational environmental performance of housing units, maximizing the social quality of life for their residents, and minimizing their life cycle cost. These novel capabilities of the developed model are expected to improve the design and construction of housing units and maximize their overall sustainability. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The overall sustainability of housing units can be maximized by optimizing their environmental, social, and economic performances [66]. This can be achieved by integrating a number of green building equipment and systems in the design and construction of housing units such as geothermal heat pumps and water-efficient faucets. While the use of these green measures can improve the environmental and/or social performances of housing units, they often lead to an increase in the initial cost of housing units and their life cycle cost. Accordingly, decision makers in the housing industry need to optimize housing design and construction decisions in order to strike an optimal/near-optimal balance among the conflicting objectives of maximizing housing operational environmental performance, maximizing social quality of life for its residents, and minimizing its life cycle cost. A number of research studies have been conducted to investigate and improve the environmental, social, and economic performances of ⁎ Corresponding author at: 205 N Mathews Ave. 3112 Newmark Civil Engineering Laboratory Urbana, IL 61801 205 N. Mathews Ave. Urbana, IL 61801, United States. Tel.: + 1 217 265 0557; fax: + 1 217 265 8039. E-mail addresses: [email protected] (A. Karatas), [email protected] (K. El-Rayes). 1 Tel.: +1 217 721 3621.

http://dx.doi.org/10.1016/j.autcon.2015.02.010 0926-5805/© 2015 Elsevier B.V. All rights reserved.

residential buildings. Several research studies focused on maximizing the operational environmental performance of buildings by optimizing their (i) building envelope variables such as window glazing type, wallto-window ratio, exterior wall type, roof type, and foundation systems [2,12,28,40,62,69,71]; (ii) HVAC systems [17,29,43]; (iii) building envelope and HVAC systems [7,9,27,31,44,74]; and (iv) building envelope, HVAC systems, lighting fixtures, and appliances [13,33]. Other studies studied focused on providing better social-quality of life for housing residents. These studies focused on improving the thermal comfort for the residents [45,51,60], daylighting quality in housing units [34,42,46], indoor air quality [10,41,57], and the level of services and amenities in housing neighborhoods [23,50,65]. Other related studies developed multi-objective optimization models for optimizing the design of the building envelope (e.g., window types and sizes) and HVAC systems (e.g., heating and cooling set points) in order to maximize housing indoor thermal comfort conditions and minimize its annual energy cost and energy usage [7,44,72]. Despite the significant contributions of the aforementioned studies, there is no study that (1) provides a comprehensive set of metrics for quantifying the collective impact of housing design and construction decisions on the overall sustainability of housing units that considers housing operational environmental performance, social quality-of-life for

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the residents, and life-cycle cost of the housing unit; and (2) optimizes housing design and construction decisions to generate optimal/nearoptimal tradeoffs among the operational environmental performance, social quality of life, and life cycle cost of housing units. To address this critical research gap, this study focus on developing a sustainability model for single-family housing units that represent 66% of the residential housing inventory in the US [63].

and life cycle cost (LCC); and (2) developing a comprehensive and practical set of criteria and metrics, as shown Table 1. This set is identified to ensure that each selected metric is simple, measurable using a quantitative value or a qualitative expression, independent of other metrics, and can be easily understood and evaluated by decisionmakers [5,36,58,68]. 3.2. Decision variables

2. Objective The objective of this paper is to develop a novel multi-objective optimization model that is capable of simultaneously maximizing the operational environmental performance (ENV) of single-family housing units, maximizing the social quality of life (SQOL) for their residents, and minimizing their life cycle cost (LCC). The model is developed in the three stages: (1) model formulation stage that identifies all relevant criteria, metrics, decision variables, objective functions, and constraints; (2) model implementation stage that performs the optimization computations using multi-objective genetic algorithms, and (3) model evaluation stage that analyzes and refines the performance of the developed model using a single-family housing unit application example. The following sections of the paper provide a brief description of these three phases of the model development. 3. Model formulation This stage of model development is formulated in four steps: (1) identifying all model criteria and their relevant metrics; (2) defining the model decision variables; (3) formulating the optimization of objective functions; and (4) identifying model constraints. 3.1. Model criteria and metrics This section presents the development of a comprehensive and practical set of sustainability criteria and metrics in order to quantify and evaluate the impact of single-family housing design and construction decisions on the three objectives of the model. This was accomplished in two steps that focused on (1) identifying all related criteria and metrics that were reported in the latest research studies on housing operational environmental performance (ENV), social quality of life (SQOL),

The model incorporates a total of thirty-three decision variables, as shown in Table 2. Each of these decision variables represents a possible selection from a set of feasible alternatives, as shown in Fig. 1. The identified list of decision variables represents housing design and construction decisions that have an impact on the aforementioned three objectives of the model and their metrics, and it covers the possible selection of the HVAC system, building envelope, lighting fixtures, appliances, water fixtures, occupant control, US Environmental Protection Agency (EPA) recommended air quality control, mechanical ventilation rate, and neighborhood quality as shown in Table 2. 3.3. Objective functions The present model integrates three objective functions to maximize the operational environmental performance of single-family housing units, maximize the social quality of life for their residents, and minimize their life cycle cost. 3.3.1. Maximizing operational environmental performance Residential units in the United States account for 18% of greenhouse gas emission, and 58% of public-supply water use [21,38,64]. These environmental challenges can be overcome by providing energy and water efficient design and construction decisions [19,39,62,69]. Accordingly, the first objective function in the model (see Eq. (1)) is designed to quantify and maximize the operational environmental performance of a single-family housing unit that represents the collective performance of the housing unit in the identified two operational environmental performance criteria: carbon footprint index (CFI), and water usage index (WTI). The objective function of ENV and its two criteria of CFI and WTI are calculated using multi-attribute utility theory (MAUT) to eliminate the impact of varying units and enable an

Table 1 Model criteria and metrics. Objectives

Criteria

Metrics

Research studies

1. Operational environmental performance (ENV)

1.1 Carbon footprint index (CFI) 1.2 Water usage index (WTI) 2.1 Thermal comfort index (TCI) 2.2 Indoor lighting quality index (LQI) 2.3 Indoor air quality index (AQI) 2.4 Neighborhood quality index (NQI)

cf1: Total amount of greenhouse gas (GHG) emissions caused by energy consumption of the housing unit and expressed in CO2 equivalent emissions (CO2e) wt1: Total amount of housing water consumption (US gal)

[20,73]

tc1: Predicted percentage of dissatisfied (PPD) index (%)

[26]

2. Social quality of life (SQOL)

3. Life cycle cost (LCC)

lq1: Annual average daylighting illuminance level (Lux) lq2: Total hours exceeding glare comfort level in a year (hours) aq1: Points achieved by performing the EPA recommended air quality control decisions aq2: Percentage of dissatisfied people (PD) from indoor air quality caused by ventilation rate (%) nq1: Education level (%) nq2: Safety level (%) nq3: Health conditions (%) nq4: Level of service and amenities (%) nq5: Economic conditions (%) nq6: Environmental conditions (%) 3.1 Life-cycle cost (LCC) lc1: Initial investment cost (US $) lc2: Operation and maintenance costs (US $) lc3: Energy and utility costs (US $) lc4: Capital replacement cost (US $) lc5: Residual value (US $)

[67]

[42] [8,70] [24] [3,25] [1,11,14,48,59]

[30,54]

A. Karatas, K. El-Rayes / Automation in Construction 53 (2015) 83–94 Table 2 Model decision variables. Housing design and construction decisions

Decision variables

HVAC system Building envelope

d1: Energy efficiency ratio of heating/cooling system d2: Window glazing type d3: Window-to-wall area ratio d4: Elevation of windows from the ground d5: R-value of exterior wall assembly d6: R-value of roof/ceiling insulation d7: R-value of foundation insulation d8: Energy efficiency (EF) and fuel type of water heating system d9: Number of light-emitting diodes (LEDs) d10: Number of compact fluorescent lighting systems (CFLs) d11: Annual energy consumption of cooking range d12: Annual energy consumption of refrigerator d13: Annual energy consumption of clothes dryer d14: Modified energy factor (MEF) and water factor (WF) of clothes washer d15: Annual energy consumption and water consumption of dishwasher d16: Water consumption of toilets d17: Water consumption of bathroom faucets d18: Water consumption of kitchen faucets d19: Water consumption of showerheads d20: Heating set point during heating season d21: Cooling set point during cooling season d22: Indoor relative humidity rate d23: Corrosion-proof of rodent/bird screens at all openings that cannot be fully sealed for pest control d24: Radon fan in the attic if the housing unit is located in EPA Radon Zone 1 d25: Radon pipe if housing unit is located in EPA Radon Zone 1 d26: Sump pump if the home does not have slab-on-grade foundation d27: CO alarms in each bedroom and the attached garage d28: Exhaust fan which has a min. installed cap of 70 cfm with automatic fan control if there is an attached garage d29: Dehumidifier and setting maximum relative humidity at 60% if the housing unit is in the warm-humid climate d30: MERV8/higher filters for HVAC d31: Exhaust fan in each bathroom and kitchen to meet ASHRAE 62.2 standards d32: Specified overall mechanical whole-house ventilation rate d33: Location of the housing unit and its neighborhood

Water heating system Lighting fixtures

Appliances

Water fixtures

Occupant control

EPA recommended air quality control

Mechanical ventilation rate Neighborhood quality

Objectives

Decision Variables

Environmental Performance

85

aggregate evaluation of performance in all criteria and metrics [15,37, 52,61]. Based on MAUT, the value of this objective function (ENV) ranges from ‘0’ to ‘1’ to represent the worst and the best operational environmental performance, respectively (see Eq. (1)). Similarly, the values of the two indices in the objective function (CFI and WTI) range from ‘0’ to ‘1’ to represent the worst and best possible performance, respectively. The following sections describe the computations of each of these two criteria. Max Operational environmental performance ðENVÞ ¼ ½w1  C FI þ ½w2  WTI

where, CFI is carbon footprint index that represents the normalized performance of the carbon footprint (CF) that is calculated using Eq. (2); WTI is water usage index that represents the normalized performance of the water usage (WT) and is calculated based on Eq. (3); and wx is the importance weight for each criterion, where wx N 0 and ∑2x = 1wx = 1. In order to provide consistency for assigning relative importance weights of each criterion (wx), the analytic hierarchy process (AHP) is utilized in the present model [56] to calculate the weights using the three AHP steps: (a) carrying out a pair-wise comparison among all criteria using the scale proposed by Saaty [55]; (b) checking for consistency; and (c) calculating the set of weights for each criterion.
CFI ¼

 f ðdt Þ−f − ðdt Þ m f þ ðdt Þ− f − ðdt Þ

ð2Þ

where, f(dt) is a function that uses EnergyPlus to calculate the total amount of greenhouse gas emission that are emitted from housing fossil fuel combustion and purchased electricity based on the selected values for each of the house decision variables d t, where ∀ t = d1, d2, ⋯, d15, d20, d21, d22, d28, d29, d31, d32 (see Table 3); f−(d1, d2, …, d12) and f+(d1, d2, …, d12) are the worst and best values for greenhouse gas emission metric (CF); m is a parameter that provides decision-makers with the flexibility of defining the shape of the CFI function to be linear, concave, or convex, where m b 1 defines a concave function, m = 1 defines a linear function linear, and m N 1 defines a convex function [35]. EnergyPlus calculates the greenhouse gas emission from on-site fossil fuels, and purchased electricity generated from a variety of fuels including natural gas, oil,

Social Quality-of-Life

Life Cycle Cost

d1

d2

d17

d18

d33

Heating/Cooling System

Window Glazing Type

Showerhead Type

Heating Set Point

Neighborhood Location

Set of Feasible Alternatives

Alternative #2 Decision Variable #2

ð1Þ

nd

This example represents the selection of the 2 alternative (High-Solar Gain Low-E Glass) for decision variable ‘d2’ (i.e. Window glazing type)

Fig. 1. Decision variables.

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Table 3 Decision variables that affect the calculation of the model criteria and metrics. Criteria

Metrics

Decision variables

1.1 Carbon footprint index (CFI) 1.2 Water usage index (WTI) 2.1 Thermal comfort index (TCI) 2.2 Indoor lighting quality index (LQI)

cf1: Amount of GHG emissions wt1: Amount of water consumption tc1: Percentage of dissatisfied index lq1: Average daylighting illuminance level lq2: Hours exceeding glare comfort level aq1: Points by the air quality control decisions aq2: PD from indoor air quality nq1: Education level nq2: Safety level nq3: Health conditions nq4: Level of service and amenities nq5: Economic conditions nq6: Environmental conditions lc1: Initial investment cost lc2: Operation and maintenance costs lc3: Energy and utility costs lc4: Capital replacement cost lc5: Residual value

d1 to d15, and d20, d21, d22, d28, d29, d31, d32 d14, d15, d16, d17, d18, d19 d20, d21, d22 d2, d3, d4

2.3 Indoor air quality index (AQI) 2.4 Neighborhood quality index (NQI)

3.1 Life cycle cost (LCC)

gasoline, diesel, coal, hydroelectric, nuclear, wind, solar power, and biomass [6].
WTI ¼

 g ðd14 ; d15 ; …; d19 Þ−g − ðd14 ; d15 ; …; d19 Þ m g þ ðd14 ; d15 ; …; d19 Þ−g − ðd14 ; d15 ; …; d19 Þ

ð3Þ

where, g(d14, d15, …, d19) is a function that uses EnergyPlus to calculate the total amount of water usage based on the selected values for each of the house decision variables of d14 (i.e., clothes washer), d15 (i.e., dishwasher), d 16 (i.e., toilet type), d17 (i.e., bathroom faucet type), d18 (i.e., kitchen faucet type), and d19 (i.e., showerheads type) as shown in Table 3; g−(d14, d15, …, d19) and g+(d14, d15, …, d19) are the worst and best values for WT. 3.3.2. Maximizing social quality of life The second objective function in the model (see Eq. (4)) is designed to quantify and maximize the social quality of life for housing residents that represents the collective performance of the housing unit in each of the aforementioned four social quality of life criteria: thermal comfort index (TCI), indoor lighting quality index (LQI), indoor air quality index (AQI), and neighborhood quality index (NQI). The objective function of SQOL, and its four criteria of TCI, LQI, AQI, and NQI are calculated using multi-attribute utility theory to eliminate the impact of varying units and enable an aggregate evaluation of performance in all criteria and metrics. The value for the objective function of SQOL ranges from ‘0’ to ‘1’, where ‘0’ represents the worst and ‘1’ represents the best social quality of life performance. Similarly, the values of the four criteria in this objective function (TCI, LQI, AQI, and NQI) range from ‘0’ to ‘1’, which represents the worst and best possible performance, respectively. The following sections describe the computations of each of these four criteria. Max Social Quality of Life ðSQOLÞ

ð4Þ

¼ ðw1  TCIÞ þ ðw2  LQ IÞ þ ðw3  AQ IÞ þ ðw4  NQIÞ where, TCI is the thermal comfort index that represents the normalized performance of the predicted percentage of dissatisfied (PPD) index; PPD index is the thermal discomfort level that predicts the percentage of people likely to feel too hot or too cold in the given thermal environment [4,26]; LQI is the indoor lighting quality index that integrates the normalized performance of two metrics of the annual average daylighting illuminance level, and hours exceeding glare comfort level in a year; AQI is the indoor air quality index that integrates the normalized

d23 to d31 d32 d33

d1 to d33

performance of two metrics of the number of points that can be earned by performing each of the EPA recommended air quality control decisions, and the percentage of dissatisfied people (PD) from indoor air quality caused by indoor ventilation rate; NQI neighborhood quality index that integrates the normalized performance of six neighborhood quality metrics of education level, safety level, health conditions, service and amenities, economic conditions, and environmental conditions; and wy is the importance weight of each criterion where wy N 0 and ∑4y = 1wy = 1. In order to provide consistency for assigning relative importance weights of each criterion (wy), the analytic hierarchy process (AHP) is utilized in the present model [56]. The calculation of each of the aforementioned four criteria (TCI, LQI, IAQ, and NQI) depends on a unique set of housing decision variables (see Table 3). The impact of these decision variables on each of the four criteria is computed using Eqs. (5)–(8) [35]. It should be noted that the thermal comfort metric of tc1, and the lighting quality metrics of lq1 and lq2 are calculated using an external energy analysis and thermal load simulation engine, EnergyPlus.

TCI ¼

f ðd20 ; d21 ; d22 Þ−f − ðd20 ; d21 ; d22 Þ f þ ðd20 ; d21 ; d22 Þ− f − ðd20 ; d21 ; d22 Þ

ð5Þ

where, f(d20, d21, d22) is a function that uses EnergyPlus algorithms to calculate the PPD index for the analyzed house based on the aforementioned decision variables of d20 (i.e., heating set point), d21 (i.e., cooling set point), and d22 (i.e., relative humidity percentage); f−(d20, d21, d22) is the worst thermal comfort performance calculated by EnergyPlus for the analyzed house (e.g., PPD = 100% which indicates that 100% of the people were dissatisfied throughout the year); and f+(d20, d21, d22) is the best thermal comfort performance calculated by EnergyPlus for the house (e.g., PPD = 0%). l

 − g ðd2 ; d3 ; d4 Þ−g ðd2 ; d3 ; d4 Þ l þ w2 þ − g ðd2 ; d3 ; d4 Þ−g ðd2 ; d3 ; d4 Þ
 hðd ; d3 ; d4 Þ−h− ðd2 ; d3 ; d4 Þ  þ 2 h ðd2 ; d3 ; d4 Þ−h− ðd2 ; d3 ; d4 Þ

LQ I ¼ w1 




ð6Þ

where, g(d2, d3, d4) is a function that uses EnergyPlus algorithms to calculate the first indoor lighting quality metric of annual average daylighting illuminance level (lq1) based on the aforementioned decision variables of d2 (i.e., window-to-wall area ratio), d3 (i.e., elevation of windows), and d4 (i.e., window type); g−(d2, d3, d4) and g+(d2, d3, d4)

A. Karatas, K. El-Rayes / Automation in Construction 53 (2015) 83–94

are the minimum and maximum values for lq1; h(d2, d3, d4) is a function that uses EnergyPlus algorithms to calculate the second indoor lighting quality metric of hours exceeding glare comfort level in a year (lq2 ) based on the aforementioned decision variables of d2, d3, and d4; h−(d2, d3, d4) and h+(d2, d3, d4) are the minimum and maximum values for lq2; wlt is the importance weight for each of the two indoor lighting quality metrics, where wlt N 0 and ∑2t = 1wlt = 1.

a

AQ I ¼ w1 

aq1 100−PD a þ w2  100 K

ð7Þ

where, aq1 is the number of points that can be earned by installing the EPA recommended AQ control equipment (d23 − d31) in Table 2; K is the total number of points that can be earned by installing all EPA recommended AQ control equipment in Table 2; PD is the percentage of dissatisfied people from indoor air quality caused by ventilation rate ‘q’ which includes mechanical ventilation rate (d32) and natural ventilation rate (nv), where q = sqrt((d32) ^ 2 + (nv) ^ 2) and PD = 395 exp(−1.83q0.25) if q ≥ 0.32 l/s, else PD = 100 % [3,25]; and waz is the importance weight for both criteria where waz N 0 and ∑2z = 1waz = 1. NQI ¼

I X

wi  U ðnqi Þ

ð8Þ

i¼1

where, U(nqi) is the utility value that represents the normalized performance of the each of the neighborhood quality (NQ) metrics in Table 3 based on the housing location (d33); I is the total number of sets of neighborhood quality (NQ) metrics in Table 3 such as education level metrics and safety level metrics; and wi is the importance weight for ith set of NQ metrics where wi N 0 and ∑Ii = 1wi = 1. 3.3.3. Minimizing life cycle cost The third objective function in the model calculates and minimizes the life cycle cost of single-family housing units, as shown in Eq. (9). Min Life Cycle Cost ðLCCÞ ¼ C ðd1 ; d2 ; …; d33 Þ

ð9Þ

where, C(d1, d2, …, d33) is a function to calculate the life cycle cost of each decision variable in the model that is dependent on the selected location of the house, including all the metrics of LCC (lc1:initial investment cost, lc2:operation and maintenance costs, lc3:energy and utility costs, lc4:capital replacement cost, and lc5:residual value). The calculation of each of these life cycle cost metrics depends on a set of housing decision variables, as shown in Table 3 and Fig. 2. It should be noted that the housing unit energy and utility costs (lc3) are calculated in the present model using an external energy analysis and thermal load simulation engine, EnergyPlus, as shown in Fig. 2. 3.4. Model constraints The model is designed to comply with all practical constraints including: (1) the type of decision variables are designed as discrete integer number for the decision variables from d1 to d22, and neighborhood location (d33), as shown in Eq. (10); (2) decision variables from d23 to d31 are designed as binary numbers to represent if EPA recommended air quality (AQ) equipment are performed or not, as shown Eq. (11); (3) the decision variable representing the mechanical ventilation rate (d32) is designed as a continuous real number to ensure that it is within a user-specified range from ‘dmax ’ to ‘dmin z z ’, as shown in Eq. (12); and (4) the summation of d9 (number of CFLs) and d10 (number of LEDs) should be less than or equal to the total number of housing lighting fixtures (LF) specified by the decision-maker, as shown in Eq. (13). dz ¼ integer;

∀z ¼ 1; 2; …; 21; 22; 33

ð10Þ

 dz ¼

max

dz

 1 → if Performed ; 0 → if Not Performed

min

≥dz ≥dz ;

∀z ¼ 32

L F ≥d9 þ d10

87

∀z ¼ 23; 24; …; 30; 31

ð11Þ

ð12Þ ð13Þ

4. Model implementation Multi-objective genetic algorithms were used to perform the optimization computations in this model due to its reported capabilities in optimizing multiple building objectives [9,44,62,69]. The model was implemented using MATLAB 2013b and coupled with an external building energy simulation engine, EnergyPlus [18]. The model was implemented in three main steps (see Fig. 2): (1) initialization step that requires the input of all relevant data set files that include all pre-defined housing design decisions and EnergyPlus input files, and identifying the model constraints and the GA search parameters such as the number of generations (G) and population size (S); (2) GA search step that executes EnergyPlus and runs the GA to calculate the criteria and metrics of each objective, and select the fittest solutions based on the calculated operational environmental performance (ENV), social quality of life (SQOL), and life cycle-cost (LCC); and (3) data output step that generates the near-optimal (i.e., non-dominated) solutions based on the computed ENV, SQOL, and LCC, and presents the tradeoff analysis for decision-makers to enable them to analyze and select optimal configurations of single-family housing design and construction decisions. 5. Performance evaluation An application example was analyzed to evaluate the present model and demonstrate its capabilities in generating optimal/near-optimal tradeoffs among the operational environmental performance, social quality of life, and life cycle cost of single-family housing units. The housing unit example was selected as B10 Benchmark which is a reference house that is built based on the 2009 International Energy Conservation Code, the 2010 Federal appliance standards, and the 2010 lighting characteristics and miscellaneous electric loads [32]. The operating conditions defining average occupant use levels and operating schedules for HVAC system, water heating system, lighting fixtures, appliances, water fixtures, exhaust fans, and mechanical ventilation rate are all based on Building America House Simulation Protocols [32,49]. The housing unit was assumed to: (1) be designed as a one-story single-family housing unit covering an area of 1800 square feet including a garage; (2) be located in Madison, WI; (3) have north–south orientation; (4) have a service life of 50 years; (5) have 30 lighting fixtures (LF) which is the average number of home lighting fixtures in the US as reported by Energy Star [22]; (6) utilize a dehumidifier to control indoor humidity levels; (7) have exhaust fans in each bathroom and kitchen to meet ASHRAE 62.2 standards; (8) have an average natural ventilation rate (nv) of 0.021 ACH; (9) have user-specified relative importance weights (wx) of the two operational environmental performance criteria of carbon footprint index and water usage index as 0.65 and 0.35, respectively; and (10) have user-specified relative importance weights (wy) of the social quality of life four criteria of thermal comfort index, indoor lighting quality index, indoor air quality index, and neighborhood quality index as 0.30, 0.15, 0.28, and 0.27, respectively. It should be noted that the model provides the capability and flexibility to consider varying user-specified weights to represent the relative importance of the aforementioned criteria that can vary from one decision-maker to another. The present optimization model integrates thirty-three decision variables, where each represents a possible selection from a set of feasible alternatives, as shown in Table 2, and Table 4. This set produces

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Fig. 2. Model implementation.

a wide search space that includes more than 2.6 quadrillion possible configurations of design and construction decisions for this analyzed housing unit. Each of these possible configurations provides a unique combination of housing operational environmental performance, social quality of life, and life cycle cost. This presents decision makers with a challenging task that requires them to search for and identify an optimal set of housing design and construction decisions from this large search space in order to simultaneously optimize the housing operational environmental performance, social quality of life, and life-cycle cost. To support decision makers in this challenging task, the present model was used to efficiently and effectively search this large space of 2.6 quadrillion possible configurations of design and construction decisions based on genetic algorithm and Pareto-optimality principles. In order

to improve the convergence quality of the developed model, the GA population size, number of generations, and crossover fraction were estimated, based on the number of decision variables in the present model, to be 300, 420, and 0.6 respectively [47,53]. The computational elapsed time for this application example was 47.5 h by utilizing one node of the University of Illinois' Golub Linux cluster where each node is configured with two Intel E5-2670, 2.6 GHz, 20 M Cache, and 8 core processors [16]. For this application example, the model was able to generate 210 near-optimal (non-dominated) solutions that represent 210 optimal/ near-optimal and unique tradeoffs among the aforementioned three optimization objectives, as shown in the three-dimensional graph in Fig. 3. These tradeoffs are also demonstrated graphically in two-

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89

Table 4 Set of feasible alternatives. Decision variables

Possible options

Life cycle costa

d1: Heating/cooling system

[Central A/C (SEER 14, EER 12, stage 1, cycling fraction 0.07); Central A/C (SEER 15, EER 13, stage 1, cycling fraction 0.07); Central A/C (SEER 16, EER 14, stage 1, cycling fraction 0.07); Central A/C (SEER 17, EER 14.4 & 13.2, stage 2, cycling fraction 0.11); Central A/C (SEER 18, EER 15.2 & 14.0, stage 2, cycling fraction 0.11); Central A/C (SEER 21, EER 17.7 & 15.3, stage 2, cycling fraction 0.11); Air source heat pump (SEER 22, 10 HSPF, varying speed, cooling cycling fraction 0.25, heating cycling fraction 0.24); Ground source heat pump, high-k soil, Enh grout (EER 20.2, COP 4.2, HX Bore 201 ft/ton, ground conductivity 1.0 Btu/h-ft-R, 0.8 grout conductivity 0.8 Btu/h-ft-R)] [Clear glass (U-value 0.49, SHGC 0.63, VT 0.63); High-solar gain low-E glass (U-value 0.39, SHGC 0.53, VT 0.51); Medium-solar-gain low-E glass (U-value 0.27, SHGC 0.46, VT 0.41); Low-solar gain low-E glass (U-value 0.26, SHGC 0.31, VT 0.46)] [10%, 12%, 15%, 18%] [2.3 ft, 2.6 ft, 3 ft, 3.3 ft] [2 × 4 steel studb, R11 fiberglass batts; 2 × 4 wood studb, R11 fiberglass batts; ICF (R11) steel ties, 3/4 in concrete stucco, foam shells; 2 × 6 wood studb, R19 fiberglass batts] Ceiling R38 fiberglass batts; Ceiling R49 fiberglass batts; Roof R49 closed cell spray foam; Roof 47.5 SIP; Roof R38 fiberglass batts; Ceiling R60 fiberglass batts Whole slab insulation R10; Whole slab insulation R20; Whole slab insulation R30; Whole slab insulation R40 Natural gas fired water heater (energy factor 0.59, tank volume 40 gal); Electric water heater (energy factor 0.90, tank volume 50 gal); Oil fired water heater (energy factor 0.62, tank volume 40 gal); Propane gas fired water heater (energy factor 0.67, tank volume 50 gal) [1, 2, …, 29, 30] [1, 2, …, 29, 30] [Conventional (244 kWh/yr); EnergyStar certified (182 kWh/year)] [Conventional (438 kWh/year); EnergyStar certified (383 kWh/year)] [Conventional 282 kWh/year; EnergyStar certified (97 kWh/year)] [Conventional MEF 2.0; WF 6.0; EnergyStar certified MEF 3.0, WF 2.7] [Conventional (318 kWh/year, 581 gal/year); EnergyStar certified (180 kWh/year, 473 gal/year)] [Conventional (1.6 GPF); WaterSense EPA Certified (1.28 GPF)] [Conventional (2.2 GPM); WaterSense EPA certified (1.5 GPM)] [Conventional (2.2 GPM); WaterSense EPA certified 1.8 GPM] [Conventional (2.5 GPM); WaterSense EPA Certified (1.75 GPM)] [67 °F, 68 °F, 69 °F, 70 °F, 71 °F, 72 °F, 73 °F, 74 °F, 75 °F] [76 °F, 77 °F, 78 °F, 79 °F, 80 °F] [45%, 50%, 55%, 60%, 65%] [Perform or not] d23: Corrosion-proof of rodent/bird screens at all openings that cannot be fully sealed for pest control d24: Radon fan in the attic if the housing unit is located in EPA Radon Zone 1 d25: Radon pipe if housing unit is located in EPA Radon Zone 1 d26: Sump pump if the home does not have slab-on-grade foundation d27: CO alarms in each bedroom and the attached garage d28: Exhaust fan which has a min. installed cap of 70 cfm with automatic fan control if there is an attached garage d29: Dehumidifier and setting maximum relative humidity at 60% if the housing unit is in the warm-humid climate d30: MERV8/higher filters for HVAC d31: Exhaust fan in each bathroom and kitchen to meet ASHRAE 62.2 standards From 55 cfm to 95 cfm [Arbor Hills, Marquette, Lake Edge]

$4227 $4576 $5496 $6098 $6821 $7689 $8196 $21,106

d2: Window glazing type

d3: Window-to-wall area ratio d4: Elevation of windows d5: Exterior wall type

d6: Roof/ceiling insulation

d7: Foundation insulation

d8: Water heater

d9: Number of CFLs d10: Number of LEDs d11: Cooking range d12: Refrigerator d13: Clothes dryer d14: Clothes washer d15: Dishwasher d16: Toilet flush d17: Bathroom sink faucet d18: Kitchen sink faucet d19: Showerhead d20: Heating set point d21: Cooling set point d22: Relative humidity d23–d31: Perform EPA recommended indoor air quality control decisions

d32: Mechanical ventilation rate d33: Location of the housing unit and its neighborhood

33 $/ft2 34 $/ft2 43 $/ft2 45 $/ft2

$6222 $6340 $54,271 $6428 $4500 $4978 $7973 $7974 $4394 $5550 $5680 $6609 $7734 $9215 $2477 $3031 $3142 $3894 1.5 $/ea. 13.5 $/ea. $853 $1170 $1393 $1793 $921 $1624 $1352 $2021 $2753 $3011 $350 $418 $142 $168 $$$185 $271 $211 $224 – – – $403 $979 $51 $2040 $387 $504 $2623 $1675 $504 – 22.0 $/ft2 31.6 $/ft2 20.8 $/ft2

a Cost data is obtained from RSMeans building construction cost data (RS Means Company, 2013); HomeDepot (Homer TCL Inc., 2014); BEopt Cost Selector (National Renewable Energy Laboratory, 2013). b 1/2 in. gypsum boards, 1/2 in. plywood, 1/2 in. wood siding.

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Solution S74 ENV=0.40 SQOL=0.83 LCC=$180,442

Solution S1 ENV=0.89 SQOL=0.63 LCC=$196,142

Solution S210 ENV=0.57 SQOL=0.61 LCC=$149,920

Fig. 3. Environmental performance—social quality of life-life cycle cost tradeoff analysis.

dimensional slices to demonstrate the tradeoffs between (1) the operational environmental performance and life cycle cost objectives, as shown in Fig. 4, and (2) the social quality of life and life cycle cost objectives, as shown in Fig. 5. Each of the generated near-optimal solutions provides a unique and optimal configuration of design and construction decisions, and optimal/near-optimal tradeoff among the three objectives of the model. The generated optimal/near-optimal solutions include three extreme solutions: (1) solution S1 that provides the maximum possible operational environmental performance (ENV = 0.89) with an associated social quality of life performance of 0.63 and life cycle cost of US $196,142; (2) S74 that provides the maximum possible social quality

of life (SQOL = 0.83) with an associated operational environmental performance of 0.40 and LCC of US $180,442; and (3) S210 that provides the least possible life cycle cost (LCC = US $149,920) with an associated operational environmental performance of 0.57 and social quality of life performance of 0.61. These three extreme solutions are analyzed in more detail in the following paragraphs to illustrate the capabilities of the developed model. The first extreme solution (S1) provided the maximum possible operational environmental performance (ENV = 0.88) by minimizing the carbon footprint and water usage of the housing unit. First, the carbon footprint was minimized in solution S1 by selecting (i) the ground source heat pump which is the most energy efficient heating/cooling

$205K

SolutionS1 ENV = 0.89 LCC = $196,142

Life-CYcle Cost LCC

$195K

Solution S35 ENV = 0.87 LCC = $177,037

$185K

$175K

$165K

Solution S210 ENV = 0.57 LCC =$149,920

$155K

$145K 0.55

0.6

0.65

0.7

0.75

0.8

Environmental Performance ENV Fig. 4. Environmental performance and life cycle cost tradeoff analysis.

0.85

0.9

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$185K

Solution S74 SQOL = 0.83 LCC = $180,442

$180K

Life-Cycle Cost LCC

91

$175K

Solution S167 SQOL = 0.81, LCC = $164,275

$170K $165K $160K $155K

Solution 210 SQOL = 0.61 LCC = $149,920

$150K $145K 0.6

0.65

0.7

0.75

0.8

0.85

Social Quality-of-Life SQOL Fig. 5. Social quality of life and life cycle cost tradeoff analysis.

system in the provided set of alternatives; (ii) a building envelope system that provides the highest insulation through including window glazing type of medium-solar gain low-E glass (U-value = 0.27, SHGC = 0.46), exterior wall type of 2 × 6 Wood Stud with R19 fiberglass batts, ceiling insulation of R60 fiberglass batts, and whole slab insulation of R40 fiberglass batts; (iii) all EnergyStar certified appliances; (iv) the lowest heating set point of 67 °F, and the highest cooling set point of 80 °F, and (v) a lower mechanical ventilation rate of 57 cfm. Second, the water usage was minimized in solution S1 by selecting (i) EnergyStar certified appliances such as clothes washer and dishwasher that have the least water consumption rate among the provided set of alternatives; and (ii) WaterSense EPA certified water fixtures. Although this solution (S1) achieved the maximum possible operational environmental performance, it provided a relatively lower social quality of life performance of 0.63 compared to solution S74 that had SQOL performance of 0.83. This relatively lower SQOL performance of S1 was caused by its selection of (1) the lowest heating set point of 67 °F, and the highest cooling set point of 80 °F that did not provide optimal thermal comfort for the housing residents; (2) window glazing type of medium-solar gain low-E glass which has the lowest visual transmittance (VT) of 0.41 that reduced the penetration of natural daylight and caused lower indoor lighting quality; (3) four out of the nine feasible EPA recommended air quality control decisions that caused a relative reduction in indoor air quality; and (4) a lower mechanical ventilation rate of 57 cfm that caused a lower level of indoor air quality. Similarly, solution S74 produced a higher life cycle cost (US $196,142) than that of solution S210 (US $149,920) because of its selection of more costly design and construction decisions to improve the operational environmental performance, as shown in Table 5, and Figs. 3 and 4. The second extreme solution (S74) maximized the social quality of life for the housing residents by achieving the possible highest improvements in the thermal comfort, indoor lighting quality, indoor air quality, and neighborhood quality. First, the maximum thermal comfort was achieved by maintaining an optimal configuration of 72 °F heating set point for the winter season, a 76 °F cooling set point for the summer season, and a 55% relative humidity rate. Second, S74 achieved maximum lighting quality by allowing maximum penetration of natural daylight while avoiding glare discomfort for the residents as a result of selecting: (i) 12% ratio of wall-to-window area, and (ii) clear glass window type which has the highest Visual Transmittance (VT) of 0.63. Third, the highest indoor air-quality was attained in solution S74 by selecting: (i) all recommended EPA air quality control decisions in Table 2; and (ii) an optimal mechanical ventilation rate of 79 cfm that provided the

lowest percentage of dissatisfied people of 4%. Fourth, the highest neighborhood quality index was achieved in S74 by selecting the site location as Marquette which has the highest neighborhood quality index (NQI = 0.90) among the three feasible alternatives. Despite the maximum social quality of life performances of these optimal decisions, they caused lower operational environmental performance (ENV = 0.40) compared to the solutions of S1 and S210 that had ENV performance of 0.89 and 0.56, respectively. This lower operational environmental performance of solution S74 was caused by higher carbon footprint and water usage of the housing unit due to the selection of the optimal heating (72 °F) and cooling set points (76 °F) for the thermal comfort of the residents which increased energy consumption. The third extreme solution (S210) minimized the life cycle cost of the housing unit (LCC = US $149,920) by reducing its initial cost, and energy and utility cost. First, the initial cost was minimized in solution S210 by selecting the least costly options including: (i) window glazing type of clear glass (U-value = 0.49), (ii) heating/cooling system of Central A/C (SEER 14, 1 stage speed), (iii) electric water heater system, (iv) all conventional appliances, (v) conventional water fixtures of toilet flush, bathroom sink faucet, and kitchen sink faucet, and (vi) the site location with the least land value. Second, the energy and utility costs was minimized in solution S120 by selecting the lowest heating set point of 67 °F during the winter season. Although these optimal housing decisions of solution S210 produced the least life cycle cost, they resulted in (1) lower operational environmental performance (ENV = 0.56) compared to Solution S1 due to increasing the carbon footprint and water usage of the housing unit by selecting the inefficient design and construction decisions; and (2) lower social quality of life performance of 0.61 compared to S74 due to reduced performances in thermal comfort, indoor lighting quality, indoor air quality, and the selection of a housing location with a lower neighborhood quality index. In addition to these three extreme solutions, the model was able to generate an additional set of 207 tradeoff solutions, where each represents a unique optimal and non-dominated tradeoff among the aforementioned three optimization objectives. Decision makers can visualize these tradeoffs using 2- or 3-dimensional graphs to select an optimal solution that best fits their specific project needs and provides the best overall tradeoff among the three objectives from their perspective. For example, analyzing the optimal tradeoffs between the operational environmental performance and life cycle cost the in Fig. 4 shows that solution S35 provides a good tradeoff between these two objectives. As shown in Fig. 4, S35 generated an operational environmental performance of 0.87 which is lower than the maximum possible performance provided by solution S1 (ENV = 0.89); however it was able to reduce

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Table 5 Sample of optimal solutions. Solution

Optimal/near-optimal solutions

ENV

SQOL

LCC

S1

{d81 : Ground source heat pump, d32 : Medium solar gain low E glass, d23 : 12 % Window to wall area ratio, d14 : 2.3 ft elevation of windows, d45 : 2 × 6 wood stud R19 fiberglass batts, d66 : Ceiling R60 fiberglass batts, d47 : Whole slab insulation R40, 11 d48 : Propane gas fired water heater, d19 9 : 19 CFLs, d10 : 11 LEDs, d211 : EnergyStar certified cooking range, d212 : EnergyStar certified refrigerator, 2 d13 : EnergyStar certified clothes dryer, d214 : EnergyStar certified clothes washer, d215 : EnergyStar certified dishwasher, d216 : WaterSense EPA certified toilet flush, d217 : WaterSense EPA certified bathroom sink faucet, d218 : WaterSense EPA certified kitchen sink faucet, d219 : WaterSense EPA certified showerhead, d120 : 67 ° F heating set point, 5 3 d21 : 80 ° F cooling set point, d22 : 55 % relative humidity, d023 : Not performed corrosion proof screens, d124 : Performed radon fan, d125 : Performed radon pipe, d026 : Not perfomed sump pump, d027 : Not performed CO alarms, d028 : Not performed exhaust fan, d129 : Performed dehumidifier, d130 : Performed MERV filter for HVAC, d131 : Performed exhaust fan in each bathroom and kitchen, 57 2 d32 : 57 cfm ventilation rate, d33 : Marquette} {d31 : Central A/C (SEER 16, Stage 1), d12 : Clear glass window, d23 : 12 % Window to wall area ratio, d14 : 2.3 ft elevation of windows, d15 : 2 × 4 steel stud R11 fiberglass batts, d26 : Ceiling R49 fiberglass batts, d27 : Whole slab insulation R20, d38 : Oil fired water heater, d79 : 7 CFLs, d23 10 : 23 LEDs, d111 : Conventional cooking range, d112 : Conventional refrigerator, 1 d13 : Conventional clothes dryer, d114 : Conventional clothes washer, d215 : Conventional dishwasher, d116 : Conventional toilet flush, d117 : Conventional bathroom sink faucet, d118 : Conventional kitchen sink faucet, d119 : Conventional showerhead, d620 : 72 ° F heating set point, d121 : 76 ° F cooling set point, d322 : 55 % relative humidity, d123 : Performed corrosion proof screens, d124 : Performed radon fan, d125 : Performed radon pipe, 1 1 d26 : Perfomed sump pump, d27 : Performed CO alarms, d128 : Performed exhaust fan, d129 : Performed dehumidifier, d130 : Performed MERV filter for HVAC, d131 : Performed exhaust fan in each bathroom and kitchen, 2 d79 32 : 79 cfm ventilation rate, d33 : Marquette} {d11 : Central A/C (SEER 14, stage 1), d12 : Clear glass window, d33 : 15 % window to wall area ratio, d24 : 2.6 ft elevation of windows d45 : 2 × 6 wood stud R19 fiberglass batts, d26 : Ceiling R49 fiberglass batts, d27 : Whole slab insulation R20, d18 : Natural has fired water heater, 19 1 d11 9 : 11 CFLs, d10 : 19 LEDs, d11 : Conventional cooking range, d112 : Conventional refrigerator, d113 : Conventional clothes dryer, d114 : Conventional clothes washer, d115 : Conventional dishwasher, d116 : Conventional toilet flush, d117 : Conventional bathroom sink faucet, d118 : Conventional kitchen sink faucet, d219 : WaterSense EPA certified showerhead, d120 : 67 ° F heating set point, d221 : 77 ° F cooling set point, d122 : 45 % relative humidity, d023 : Not performed corrosion proof screens, d024 : Not performed radon fan, d025 : Not performed radon pipe, d026 : Not perfomed sump pump, d027 : Not performed CO alarms, d028 : Not performed exhaust fan, d129 : Performed dehumidifier, d030 : Not performed MERV filter for HVAC, d131 : Not performed exhaust fan in each bathroom and kitchen, 1 d68 32 : 68 cfm ventilation rate, d33 : Arbor Hills}

0.89

0.63

US $196,142

0.40

0.83

US $180,442

0.57

0.61

US $149,920

S74

S210

the life cycle cost of the housing unit to US $177,037 compared to the US $196,142 that was achieved by solution S1. Similarly, analyzing the generated optimal results in Fig. 5 shows that solution S167 provides a good tradeoff between the two objectives of social quality of life and life cycle cost. Solution S167 generated a social quality of life performance of 0.81 which is lower than that the maximum achieved by solution S74 (SQOL = 0.83); however it reduced the life cycle cost of the housing unit to US $164,275 compared to the US $180,442 that was achieved by solution S74. Accordingly, this wide range of generated optimal tradeoffs can be analyzed by decision-makers in order to identify an optimal solution that best addresses the specific needs of their project.

6. Summary and conclusion This paper presented a novel multi-objective optimization model for optimizing housing design and construction decisions to simultaneously maximize the operational environmental performance of single-family housing units, maximize the social quality of life for their residents, and minimize their life cycle cost. The model was developed in three stages: (1) model formulation stage that identified all relevant criteria, metrics, decision variables, objective functions, and constraints; (2) model implementation stage that performed the optimization computations using multi-objective genetic algorithms, and (3) model

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evaluation stage that analyzed and refined the performance of the developed model using a single-family housing unit application example. The analysis results illustrated the new and innovative capabilities of the model in generating near-optimal solutions, where each provides a unique and optimal configuration of design and construction decisions, and an optimal tradeoff among the three objectives of the model. The model was able to generate 210 near-optimal tradeoff solutions including three extreme solutions that provide the maximum housing operational environmental performance, the maximum social quality-of life for its residents, and the minimum life cycle cost of the housing unit. These new capabilities enable decision makers in generating and analyzing optimal tradeoffs among objectives of the model to identify optimal configurations of design and construction decisions of single-family housing units that best fits their specific demands. Notation ENV SQOL LCC CFI

operational environmental performance social quality of life life cycle cost normalized performance of the housing carbon footprint that is represents the total greenhouse gas emissions (i.e., CO2, CH4, and N2O) caused by energy consumption of the housing unit based on the selected values for each of the house decision variables (d1 to d14) WTI normalized performance of the housing water usage that represents the total amount of water consumption based on the selected values for each of the house decision variables from d11 to d16 TCI normalized performance of the residents' thermal comfort that is calculated based on predicted percentage of dissatisfied index for the analyzed house based on the aforementioned decision variables of d1, d2, and d3 lq1 annual average daylighting illuminance level lq2 hours exceeding glare comfort level in a year LQI normalized performance of the residents' indoor lighting quality that is calculated based on lq1 and lq2 aq1 the total number of points that can be earned by performing EPA recommended air quality decisions q ventilation rate nv natural ventilation rate aq2 percentage of dissatisfied people from indoor air quality caused by q AQI normalized performance of the residents' indoor air quality that is calculated based aq1 and aq2 nq1 education level of the neighborhood that quantifies the educational attainment, school proximity, achievement level of neighborhood schools in NAEP assessments, college enrollment rate, and high mobility students nq2 safety level of the neighborhood that measures property, society, and violent crime rates nq3 health conditions of the neighborhood that quantifies the availability of local health services and birth weight of newborns nq4 services and amenities of the neighborhood that measures local transportation service conditions, availability of retail services, parks, open spaces, and recreation facilities within the neighborhood boundaries nq5 economic conditions of the neighborhood that measures the income inequality and local business conditions nq6 local environmental conditions of the neighborhood that measures the overall air, water, and soil quality in the neighborhood of the housing location NQI normalized performance of the housing neighborhood quality calculated based on nq1, nq2, nq3, nq4, nq5, and nq6 C(d1, d2, …, d33, V) performance the LCC of the house including metrics based on the house decision variables (d1 to d33) and all the pre-defined housing features ‘V’

d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 d16 d17 d18 d19 d20 d21 d22 d23 to d31 d32 d33 wx wy Qfan Afloor Nbr

93

heating/cooling system window glazing type window-to-wall area window elevation exterior wall type roof/ceiling insulation foundation insulation water heater number of light-emitting diodes number of compact fluorescent lighting systems type of cooking range type of refrigerator type of clothes dryer type of clothes washer type of dishwasher type of toilet flush type of bathroom sink faucet type of kitchen sink faucet type of showerhead heating set point cooling set point relative humidity percentage installation of EPA recommended air quality equipment mechanical ventilation rate neighborhood location importance weight of each ENV criteria importance weight of each SQOL criteria mechanical ventilation rate of the housing unit total floor area (ft2) of the housing unit number of bedrooms of the housing unit

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